math help?

Question

consider these three equations: Y= 0.625^x, Y=0.375^x, and 1-0.5^x


a. Sketch graphs of the equations on one axes.


its my sister's problem so if anyone can help her or explain how to do this in the best way that you can it would help.

Answer 1

First, you want to get some idea of the scales. So let's try the three simplest points to plot: X = -1, X = 0, X = 1.

Looking at the Y axis:

When X = 0, the first two equations will have value 1 and the third will have value 0.

For X = 1, all three will have values between 1 and 0

For X = -1, things get interesting. The first two have values greater than 1, while the third has a negative value.

Also, a^x is a very smooth function. That suggests that you really only need two more points, for X = -2 and X = 2.

This gives you values that can be easily computed on a 4-function calculator, but will still give you a good idea of the behavior of these functions.

Recall that:

a^0 = 1
a^1 = a
a^2 = a times a
a^(-x) = 1/a^x